On a Furstenberg-Katznelson-Weiss type theorem over finite fields
Combinatorics
2008-07-18 v1
Abstract
Using Fourier analysis, Covert, Hart, Iosevich and Uriarte-Tuero (2008) showed that if the cardinality of a subset of the 2-dimensional vector space over a finite field with q elements is >= rq^2, with q^{-1/2} << r <= 1 then it contains an isometric copy of >= crq^3 triangles. In this note, we give a graph theoretic proof of this result.
Keywords
Cite
@article{arxiv.0807.2849,
title = {On a Furstenberg-Katznelson-Weiss type theorem over finite fields},
author = {Le Anh Vinh},
journal= {arXiv preprint arXiv:0807.2849},
year = {2008}
}